I would move the H264 files in question into a new folder within the current capture scratch location.
I would then use the PR422(or other PR flavor) Apple preset in Compressor to convert the files in the folder.
The preset will not change the size, length, frame rate etc. just the codec.
Export the new PR to the previous H264 location before moving into the folder.
You can either name them in Compressor or after the fact in the exported location but either way the new file names need to match the H264 name.
Final Cut should auto reconnect to the new files but worst-case you may have to manually reconnect to the new files as FC could still be able to connect to the new H264 folder. You could also move the H264 files out of the capture scratch folder before compressing but I like to hang onto all source file flavors just in case I have to go back.